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Hello,
I've seen some people asking about the rating comparisons between sites and formats. The video below is a very well sourced and unbiased look at these data. It also compares each site/format at each time control. There are sources in the comments of the video.
The most interesting points to me was that it seems that Chess.com ratings are quite close to OTB ratings. Lichess ratings are highly inflated, although as your rating increases, the gap between these ratings gets smaller. Very interesting.
https://www.youtube.com/watch?v=4i2TqBVi9Lo